In the Fractal world there are so many different amps that produce clean tones, and produce different clean tones that work better or worse with overdrives.
For example, tube screamers typically sound best to most people in front of a normal Fender style circuit, not just that but they really sound best when the amp is overdriving at least a little bit, not when the amp is set crystal clean. The famous sound people think of is a Fender overdriving a bit while the tube screamer slams the front of it and molds perfectly for a very cool sound.
Lots of people love David Gilmour type overdrive sounds, he is an example of a person who has used a whole lot of different type of gear.
Everything from, Fender band commander, bassman, to the famous Hiwatts.
So the point being, there is no one best. It all depends what sound you are going for. However a general guide is, certain overdrives like a tube driver especially the 4 knob model, are very scooped in the EQ compared to a tube screamer. Amps with more mid range typically sound better with a tube driver. Bassman. JTM45. Hiwatt. Etc. Tube screamers are heavy on the mids which is why most people prefer them through non bassman style Fenders and similar circuits with generally less mid range. Fuzz pedals like a big muff are also pretty scooped in the EQ and sound better with more mid rangey amps.
Another thing I think people should consider with the Axe FX is you do not need to use overdrive / distortion pedals anymore for a lot of sounds people use them for. Especially ones that are ones meant to emulate a amp sound to begin with. Why not use the real amp model in that case?
I think that covers everything. Try everything and have fun doing it.
